Age-Stratified Model to Assess Health Outcomes of COVID-19 Vaccination Strategies, Ghana

We assessed the effect of various COVID-19 vaccination strategies on health outcomes in Ghana by using an age-stratified compartmental model. We stratified the population into 3 age groups: <25 years, 25–64 years, and ≥65 years. We explored 5 vaccination optimization scenarios using 2 contact matrices, assuming that 1 million persons could be vaccinated in either 3 or 6 months. We assessed these vaccine optimization strategies for the initial strain, followed by a sensitivity analysis for the Delta variant. We found that vaccinating persons <25 years of age was associated with the lowest cumulative infections for the main matrix, for both the initial strain and the Delta variant. Prioritizing the elderly (≥65 years of age) was associated with the lowest cumulative deaths for both strains in all scenarios. The consensus between the findings of both contact matrices depended on the vaccine rollout period and the objective of the vaccination program.

Susceptible individuals become fully vaccinated (move to the V compartment) at a rate of v per day, while the vaccine is assumed to have an efficacy (or effectiveness) of σ.

Model parameters
In our model, after susceptible individuals are exposed, the latent period, which is the period from exposure to infectiousness, is 1/k and is assumed to have a mean of 1.85 days (3,4). Once exposed, a third (δ) of individuals become pre-symptomatically infected, and the rest (1-δ) become asymptomatic (5,6). The mean pre-symptomatic period, 1/c, is assumed to be 2.9 days (7  (13). Two doses of the AstraZeneca COVID-19 vaccine were reported to have an efficacy (σ) of 0.745 (14). This value would also be updated in our scenario analysis of the delta variant. Immunity is acquired from either natural infection or vaccination.
Vaccination-induced immunity offers protection from infection for six months (180 days) and wanes at a rate of χ, while that from natural infection, w, is about one year (365 days) (15). The rate of vaccination, v, is varied depending on the scenario. Once immunity wanes, individuals move back to the susceptible compartment. Details of model parameters are found in Appendix 1 Table 1.

Age-stratification
The aforementioned SEPIARD-V model was further developed into an age-stratified model. disproportionately affected the younger population with a mean age of 37.9 years, with the majority (56.64%) between 31 and 64 years (17). According to Ghana's demographics, 56.08% of the population is below 25 years, and 4.44% are 65 years or above (18). Therefore, the population was stratified into three groups: <25 years, 25-64 years, and 65+ years.

Age-stratified model formulation
An age-stratified compartmental model assumes that population mixing is not homogeneous and the numbers of contact between members of age groups follow a specified contact matrix. The number of secondary cases caused by an infectious individual in a totally susceptible population is commonly known as the basic reproduction number. In the context of a heterogeneous-mixing model, the basic reproduction number is also known as a basic reproductive ratio and is the largest eigenvalue of the next generation matrix (NGM) (19). Following the work of Towers and Feng (20), the reproduction number of an age-stratified model is equal to the product of the transmission coefficient β, the mean duration of infectiousness, and the largest eigenvalue of a matrix M that is defined by its elements = � �, where Cij is the contact matrix, and Ni and Nj are the numbers of individuals in age groups i and j respectively (21).

Contact matrices used
Due to the strong evidence of assortative mixing between age groups in the general population of Uganda (22) and Kenya (23), the contact matrix of the population was considered in the modeling of vaccination allocation strategies in Ghana. As reported by Waroux and colleagues, the contact patterns of Uganda were adopted in this study because their matrix corresponds to the population groups used in this study (below 25 years, 25-64 years, and 65 years or above). There is also a similarity in the proportion of age structure between Uganda and Ghana. This contact matrix was then corrected for reciprocity using methods described by Melegaro in their study in Zimbabwe (26).
Case-fatality ratio in the age-stratified model The age-specific fatality ratios were calculated using data from Odikro and colleagues' study on the epidemiology of COVID-19 outbreak in Ghana (27 among the elderly (65+) (27,28). Finally, we calculated the age-specific case fatality ratios as the ratio between the number of deaths in each age group by the number of cases in each age group.
All other variables except the vaccination rate remained the same as described in Appendix 1 Table 1.

Model initialization
The model's system of ODE was solved following the Runge-Kutta 4 method in the deSolve package in R version 4.1.1 (R Core Team; https://www.r-project.org/). To keep it simple, the population size of Ghana, N, was set to 30,800,000. We also assumed that for the base case scenario, at the beginning of the simulation, I =1, A=0, P=0, D=0, and V=0. We accounted for the age-specific seroprevalence of SARS-CoV-2 using estimates from Quarshie and colleagues in August 2020 (29). We, therefore, assumed that 17.5% of persons below 25 years, 43.6% of those between 25-64 years, and 18% of 65+ persons had been infected at the beginning of the simulation. These individuals were in the recovery compartment at the beginning of the simulation. The model was run for 500 days to allow enough time for the first wave of the epidemic to die out and observe when the second wave began to emerge.

Outcomes
The cumulative number of infections and deaths averted in the general population was estimated and compared for each scenario. Furthermore, the percent of the population who were symptomatic at the peak, ever infected (cumulative infections), and cumulative deaths were assessed. The percentage of cumulative infection could exceed 100% because as immunity waned, individuals would become susceptible again to repeated infections.

R code
The R code used for simulation in this study is provided in Appendix 2.